log a x = log a z if and only if x = z. If a > 1 then the logarithmic functions are monotone increasing functions. That is, log a x > log a z for x > z.

Is Log always increasing?

Now we consider a logarithmic function. ... The graph is curved upward where the function is defined (positive real numbers), in a way that it is always increasing. Any logarithm with a positive base will have a similar pattern. Example 3: Explain why x=0 is the only solution to 3x=1.

How do you know if a log is increasing or decreasing?

State the domain, range, and asymptote. Before graphing, identify the behavior and key points for the graph. Since b = 5 is greater than one, we know the function is increasing. The left tail of the graph will approach the vertical asymptote x = 0, and the right tail will increase slowly without bound.